LINR 1 | Lesson 1 | Practice (Solutions)

Practice (Solutions)

Tables

Complete each section to show your understanding for linear patterns.

The following tables represent linear patterns. The tables are created using Desmos.com.

Table 1
Table 2
Table 3
  1. Find the missing values in each table.
    • Table 1: (3, 7) and (12,15)
    • Table 2: (4, 9) and (21, -42)
    • Table 3: (-2, 4) and (8, 24)
  2. Graph each table on a coordinate plane.
  3. Calculate the slope using the table.
    • Table 1: change in \(y\) is 4 and change in \(x\) is 1, i.e. slope is 4
    • Table 2: change in \(y\) is -3 and change in \(x\) is 1, i.e. slope is -3
    • Table 3: change in \(y\) is 2 and change in \(x\) is 1, i.e. slope is 2
  4. Calculate the slope using the graph.
  5. Determine the point of the \(y\) intercept.
    • Table 1: (0,-5)
    • Table 2: (0,18)
    • Table 3: (0,8)
  6. Write an equation to determine the \(y\)value given any \(x\)-value.
    • Table 1 equation: \(y = 4x -5\)
    • Table 2 equation: \(y=21 – 3x\)
    • Table 3 equation: \(y= 2x + 8\)

Patterns

Given the growth pattern shown in Figure 2 and Figure 4.

  1. Draw Figure 3.
    • Figure 3 has 3 rows of 6, so a row of 6 is added to Figure 2.
  2. Explain the growth pattern.
    • 6 is added each time.
  3. Determine the number of squares in Figure 0.
    • Figure 0 has 1 square.
  4. Write the equation to represent the number of squares for any figure.
    • \(1 + 6n\), where \(n\) is the figure number.
  5. Using the context of growth patterns, explain why \(m\) represents the slope and \(b\) represents the \(y\)-intercept in the slope-intercept formula \(y=mx+b\).
    • The slope is 6 since, 6 squares are added to create the next figure. To find the \(y\)-intercept we need to find the number of squares in Figure 0 which can be found by subtracting 6 squares from Figure 2 to find Figure 1, and another 6 squares from Figure 1 to find Figure 0, or 13-6-6 = 13-12 = 1. Therefore 1 is the \(y\)-intercept.

A given linear pattern has 10 squares in Step 3.  The pattern grows by -4 squares every 2 steps.

  1. Create a table for this pattern.
  2. Calculate the slope to represent the growth for this pattern.
    • Slope is -4
  3. Calculate the equation to calculate the number of squares for each step.
    • \(y = 22 – 4x\)

Return to Practice

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